Dynamic determination of the dimension of PCA calibration models using F‐statistics

Abstract

Owing to experimental measurement errors, determination of the proper dimension of calibration models is difficult. Cross-validation is a common approach for this purpose; however, if data evaluation is based on PCA only without consideration of sample concentrations, this computationally expensive method cannot be applied. In this study a statistical method for determining the proper dimension of PCA calibration models is presented from the viewpoint of multivariate regression analysis considering only measured data. For this iterative algorithm, individual principal components are included stepwise in a reduced model, which is subsequently tested against the full model including all principal components. This algorithm can be individually applied for optimized data evaluation to every measured data vector such as an optical spectrum of chemical analyte. This comparison is performed by an F-test comparing estimates of residual variance of a measurement spectrum determined from the reduced and the full model. This approach determines a lack of fit due to insufficient principal components. If no lack of fit is evident for a certain reduced model, it is considered that a sufficiently large model has been found and inclusion of additional principal components is stopped. Hence the resulting reduced calibration model includes only statistically significant principal components (PCs) and determines the minimum number of required PCs for a given measurement spectrum. The proposed algorithm is initially investigated using simulated data and subsequently applied to three different experimental sets of spectra. It is shown that for synthetic data at reasonable noise levels the correct number of principal components can be determined in most cases. The experimental examples demonstrate that the number of principal components determined by the proposed algorithm is slightly larger than a user would select manually by subjective visual inspection. As one result, the algorithm is able to detect small but significant spectroscopic features of experimental data which would otherwise be neglected.

Quality control of herbal medicines

“…Thus, the chemical pattern recognition methods, such as K-nearest neighbors (KNN) [190,192] and soft independent modeling of class analogy (SIMCA) [193], etc. should be taken into consideration for reasonable definition of the class of the herbal medicine [194][195][196]. In fact, several researchers in China had worked on the concepts of using chemical analytical and chromatographical fingerprinting to measure the consistency of raw Chinese medicinal herbs and composite formula with the application of fuzzy clustering analysis of HPLC pattern in the early 1990s [225].…”

“…The quality of herbal objects was further evaluated, and the causes of this fact have been explained from a chemical point of view. The other method [220] is based on secured principal component regression (sPCR) that was originally developed for detecting and correcting uncalibrated spectral features newly emerging in spectra after the PCR calibration [196,197]. It can detect and consider unexpected chromatographic features for quality evaluation of herbal samples from the point of view of analyzing fingerprint residual.…”

Secured PCR (sPCR) for detection and correction of PCR calibration model failures induced by uncalibrated spectral features

“…A method for selecting R based on testing the significance of PCs by means of an F-test is proposed in Ref. [16]. After selecting R, P (N Â R) and T T (R Â K) are abridged to the number of relevant PCs without changing the notation in the following.…”

Peer Reviewed: Mid-IR Fiber-Optic Sensors

“…This task includes deconvoluting overlapping responses from multiple components, correcting for drift, and presenting quantitative results on individual analytes. This problem is currently being tackled from two sides: higher-order sensors based on orthogonal transduction schemes integrated into one device (6) and the application of multivariate chemometric calibration and data evaluation techniques for reliable evaluation of complex sensor responses (7 ).…”